Inventory routing problems: an introduction
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Inventory routing problems: an introduction Luca Bertazzi • M. Grazia Speranza
Received: 11 June 2012 / Accepted: 2 November 2012 Ó Springer-Verlag Berlin Heidelberg and EURO - The Association of European Operational Research Societies 2012
Abstract In this tutorial paper, we introduce the inventory routing problems (IRPs) with examples, we classify the characteristics of an IRP and present different models and policies for the class of problems where the crucial decision is when to serve customers. We call this class the problems with decisions over time only. The contributions are on the single link case, i.e., the problem where products are shipped from a supplier to a customer with capacitated vehicles, and on the IRPs with direct shipping. We overview the pioneering papers that appeared in the eighties, the literature on the single link and direct shipping problems, and cite the surveys and the tutorials available. Keywords
Tutorial Survey Single link Direct shipping Worst-case analysis
Introduction It is well known that whenever a problem needs to be optimized, the decomposition of the problem into subproblems yields a sub-optimal solution. However, large problems are difficult to tackle and optimization models aim at optimizing a small part of a much more complex system. Whereas in several situations, the problem is relatively independent of the rest of the system, in other situations this is not the case. In general, modeling more comprehensive problems creates the opportunity for more savings. In transportation and logistics, a trend in the direction of considering more and more comprehensive systems can be observed both in practice and in the academic world. L. Bertazzi M. G. Speranza (&) Department of Quantitative Methods, University of Brescia, Brescia, Italy e-mail: [email protected] L. Bertazzi e-mail: [email protected]
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L. Bertazzi, M. G. Speranza
The concept of logistics has evolved over time to include more and more company functions and has inspired the concept of supply chain management that aims at including more companies in the integration process. The advance of information systems, the availability of data and the rise of the Internet have favored this direction. Restricting the attention to optimization models in transportation and logistics, one can observe the growth of contributions in the modeling of systems that were traditionally decomposed and solved separately. This is also due to the advances in solution methods, both exact and heuristic, and the increased power of commercial software for linear programming (LP) and mixed integer linear programming (MILP) models. In this paper, we introduce, motivate and survey the area of an inventory routing problems (IRPs), an area where the first contributions date back to the eighties and that has been constantly growing over time. The adoption by several companies of the so-called Vendor Managed Inventory (VMI) technique in supply chain management has partially driven the research in this area. Thousands of pap
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